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We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…

We study point sets arising from cut-and-project constructions. An important class is weak model sets, which include squarefree numbers and visible lattice points. For such model sets, we give a non-trivial upper bound on their pattern…

In this note, we prove that intrinsic characteristic classes of Lie algebroids - which in degree one recover the modular class - behave functorially with respect to arbitrary transverse maps, and in particular are weak Morita invariants. In…

We study a ring of weak Jacobi forms indexed by integral lattices of rank two. We find an explicit finite set of generators of this ring and give a dimension formula for weak Jacobi forms of rank two lattice index.

One of the prominent current challenges in complexity theory is the attempt to prove lower bounds for $TC^0$, the class of constant-depth, polynomial-size circuits with majority gates. Relying on the results of Williams (2013), an appealing…

The convergence of DP Fourier series which are neither strongly convergent nor strongly divergent is discussed in terms of the Taylor series of the corresponding inner analytic functions. These are the cases in which the maximum disk of…

We introduce a double staircase construction $T$ and show that the weak closure of $\{T^n\}$ is $\{\int, 2^{-m}T^n+(1-2^{-m})\int \ : m\in\N,\ n\in \Z\}.$

We establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to…

We study the uniform computational content of the Vitali Covering Theorem for intervals using the tool of Weihrauch reducibility. We show that a more detailed picture emerges than what a related study by Giusto, Brown, and Simpson has…

We prove a formula for the Bloch-Kato logarithm of the bottom class in the Asai-Flach Euler system associated to a quadratic Hilbert modular form. We show that this can be expressed as a value, outside the interpolation range, of the p-adic…

We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature…

We prove that two dual operator algebras are weak$^*$ Morita equivalent if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak$^*$-continuous on appropriate morphism…

We introduce a new framework to deal with rough differential equations based on flows and their approximations. Our main result is to prove that measurable flows exist under weak conditions, even solutions to the corresponding rough…

We show that diagrammatic sets, a topologically sound alternative to polygraphs and strict $\omega$-categories, admit an internal notion of equivalence in the sense of coinductive weak invertibility. We prove that equivalences have the…

Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street's weak wreath product construction. That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories…

In this article a technique for constructing $p$-ary bent functions from near-bent functions is presented. Two classes of quadratic $p$-ary functions are shown to be near-bent. Applying the construction of bent functions to these classes of…

This thesis is devoted to the proof of a theorem showing the existence of a closed model category structure for weakly enriched categories. It requires first of all the definitions of weakly enriched categories and equivalences of weakly…

We study a class of weakly coupled Hamilton-Jacobi systems with a specific aim to perform a qualitative analysis in the spirit of weak KAM theory. Our main achievement is the definition of a family of related action functionals containing…

In this paper the lightface $\Pi^{1}_{1}$-Comprehension axiom is shown to be proof-theoretically strong even over $\mbox{RCA}_{0}^{*}$, and we calibrate the proof-theoretic ordinals of weak fragments of the theory $\mbox{ID}_{1}$ of…

We study the quantum transport through networks of diffusive wires connected to reservoirs in the Landauer-B\"uttiker formalism. The elements of the conductance matrix are computed by the diagrammatic method. We recover the combination of…